Concepts Pt 4.

Question 1

To find how many factors 720 has

Answer 1

first find its prime factorization: . All of its factors will be of the form . Now there are five choices for a (a= 0, 1, 2, 3, or 4), three choices for b (b = 0, 1, or 2), and two choices for c (c= 0 or 1). The total number of factors is therefore 5 x 3 x 2 = 30. 720 has 30 factors.

Question 2

The least common multiple

Answer 2

The least common multiple of two numbers is the smallest positive integer with both numbers as a factor. The LCM of 4 and 6 is 12 – it is the smallest number that has both 4 and 6 in its divisors. The LCM of 9 and 15 is 45; the LCM of 7 and 21 is 21, because 21′s factors are 1, 3, 7, and 21. To find the LCM of any two numbers, take the prime factorization of each number, find what prime factors appear in both, and multiply one of each of the shared primes and then by all the unshared primes. So for example, 12 = 2 x 2 x 3, and 56 = 2 x 2 x 2 x 7, so the LCM of 12 and 56 is (2 x 2) [shared primes] x 3 [12’s unshared primes] x (2*7) [56’s unshared primes] = 168. The largest possible LCM for any two numbers is one multiplied by the other.

Question 3

Divisibility 3

Answer 3

Divisibility

3 : sum of digits divisible by 3

Question 4

Divisibility 4

Answer 4

4 : the last two digits of number are divisible by 4

Question 5

Divisibility 6

Answer 5

6 : even number and sum of digits is divisible by 3

Question 6

Divisibility 8

Answer 6

8 : if the last three digits are divisible by 8

Question 7

Divisibility 9

Answer 7

9: sum of digits is divisible by 9